US6687363B1 - Method of designing signaling networks for internet telephony - Google Patents
Method of designing signaling networks for internet telephony Download PDFInfo
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- US6687363B1 US6687363B1 US09/517,658 US51765800A US6687363B1 US 6687363 B1 US6687363 B1 US 6687363B1 US 51765800 A US51765800 A US 51765800A US 6687363 B1 US6687363 B1 US 6687363B1
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04Q—SELECTING
- H04Q3/00—Selecting arrangements
- H04Q3/64—Distributing or queueing
- H04Q3/66—Traffic distributors
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04M—TELEPHONIC COMMUNICATION
- H04M7/00—Arrangements for interconnection between switching centres
- H04M7/006—Networks other than PSTN/ISDN providing telephone service, e.g. Voice over Internet Protocol (VoIP), including next generation networks with a packet-switched transport layer
Definitions
- FIG. 1 shows a pair of telephones 10 , 15 , each connected to bearer network 20 through a respective local exchange switch 25 , 30 which is, for example, a Lucent Technologies 5ESS switch.
- STPs Signal Transfer Points
- PDD Post-Dialing Delay
- internet telephony A newer kind of telephony, referred to as internet telephony, is rapidly growing in importance.
- the substance of the telephone call is transmitted through a network of internet routers in the form of packetized signals which conform, e.g., to the TCP/IP protocol.
- a network of internet routers referred to below as, simply, “the internet,” is indicated in the figure as network 40 .
- call setup involves the establishment of an IP session instead of a switched circuit.
- signalling messages are sent through a parallel network of software switches, such as Lucent Technologies Softswitches.
- a software switch network is indicated in FIG. 1 as network 45 .
- the software switches of network 45 do not intercommunicate exclusively through dedicated hardware. Instead, they use the resources of the internet itself for intercommunication.
- the software switch of internet telephony in current implementations is a virtual network.
- a prefix When a customer wishes to place an internet telephone call, he includes in the dialed number a string, referred to as a prefix, indicative of a particular provider of internet telephone service.
- a prefix typically consists of a seven-digit string included just before the seven-digit local telephone number being dialed.
- the internet prefix is analogous to the seven-digit access code for long-distance carriers.
- the internet prefix is interpreted at the originating local exchange switch, e.g., switch 25 .
- the call is sent to the internet and not to the conventional telephone network.
- switch 25 sends call data directly to software switch network 45 , and also to an associated Packet Voice Gateway (PVG) 50 .
- PVG Packet Voice Gateway
- the PVG sends data to internet router network 40 and to software switch network 45 .
- the local exchange switch at the receiving end e.g., switch 30 , receives data directly from network 45 and from an associated PVG 55 .
- PVG 55 receives data from network 40 and from network 45 .
- switch 30 connects to telephone 15 .
- FIG. 2 Further information about the flow of signals is illustrated in FIG. 2 . Elements common to FIGS. 1 and 2 bear the same reference numerals in both figures.
- Analog signals represented in the figure by solid lines, flow between each telephone 10 , 15 and the corresponding local exchange switch 25 , 30 .
- Analog signals also flow between each local exchange switch and a corresponding PVG 50 , 55 . Included among the functions of the PVG is analog-to-packet conversion.
- packet signals embodying the substance of the telephone call represented in the figure by broken lines, flow between PVGs 50 , 55 and the internet IP routers. Shown in the figure are the origination router, e.g., router 60 , and the destination router, e.g., router 65 .
- Signaling messages pass among the multiple switches of the software switch network. Shown in the figure are origination and destination software switches 70 and 75 . Also shown are two intermediate software switches 80 and 85 . Origination software switch 70 also exchanges signaling messages with origination local exchange switch 25 and with origination PVG 50 . Destination software switch 75 also exchanges signaling messages with destination local exchange switch 30 and with destination PVG 55 .
- Each software switch includes a plurality of Call Coordinators (CCs) 100 and a Device Server (DS), such as an SS 7 device server. Shown in the figure are DS 90 , associated with orgination software switch 70 , and DS 95 , associated with destination software switch 75 . For simplicity of presentation, the device servers associated with the intermediate software switches are not shown in the figure.
- CCs Call Coordinators
- DS Device Server
- the DS within each software switch processes the call set-up strings when that switch is the origination or destination switch for a call.
- the CCs set up the origin and destination PVGs.
- the DS also performs round-robin scheduling or other load-balancing operations among the various CCs of that switch.
- each CC within an individual switch communicates with the DS of that switch.
- the CCs within an individual switch do not typically communicate directly with each other.
- Each CC of a given software switch is desirably connected to one or more CCs of one or more other switches, such that collectively, the interconnections among all of the CCs span the entire software switch network. That is, the network should be able to transmit set-up data for a call originating at any given software switch to any other software switch via a series of hops from switch to switch through the network.
- a typical world-wide network for internet telephony may have as many as 200 or more software switches.
- each software switch will have several tens of CCs, exemplarily about 50 CCs.
- CCs exemplarily about 50 CCs.
- each hop consumes some time, which may be as much as 100 ms or more. If excessive delay accumulates during a transit of the network, call set-up may not be achieved in time to satisfy the two-second limit on PDD. Therefore, it is desirable for the diameter of the network, i.e., the number of hops separating the most distant pair of CCs, to be limited to a small number, such as two hops.
- the links between CCs are virtual links. Under TCP/IP and certain other protocols, for example, these links are of the kind referred to as sockets.
- a socket is a software construct that permits communication between computational processes.
- a disadvantageous property of sockets in software switches is that for each CC, delay and overhead penalties increase with the number of open sockets belonging to such CC. The delay and overhead penalties are not proportional to the number of open sockets, but instead have a rate of increase that is faster than proportionality.
- a second desirable feature of a CC network is that the number of links ending on a given CC (i.e., the degree of that CC) should be relatively small.
- a computational aide to designing an advantageous CC network is available in the form, for example, of an Integer Program.
- an Integer Program By solving an Integer Program, it is possible to generate a network that conforms to the stated requirements.
- the computational complexity of such a solution grows exponentially in the total number of CCs in the network. Thus, for all but very small networks, it is intractable to solve an IP at reasonable time and expense.
- our invention involves treating the network of CCs, initially, as a collection of isolated points, one point for each CC. Then, links are added between pairs of CCs, excluding fraternal pairs, i.e., pairs lying within the same switch. The links are added randomly, but with a particular probability p, which may be different for different pairs. That is, between each admissible pair (i.e., each pair not lying within the same switch), a link is either added or not added. Whether the link is added depends, in effect, upon the outcome of a loaded coin toss, in which the probability of a positive outcome is p.
- the first network to be generated is satisfactory as to diameter and maximum degree.
- the random network that has been constructed is improved further in a post-processing step.
- links are added between those admissible pairs that are still separated by more than two hops.
- the further links are added until all admissible pairs are connected by at most two hops.
- the invention in one aspect involves performing, at least once, a step of randomly assigning edges to pairs of vertices of a graph wherein each vertex represents a node of the communication network.
- the random assignment is carried out such that: (i) any fraternal pair has zero probability of being assigned an edge, but all admissible pairs have a finite probability of being assigned an edge; and (ii) at least one resulting graph, denominated a low-degree graph, has a maximum degree less than 2 ⁇ square root over (n(nl n)) ⁇ .
- the invention further includes adding edges, if any are needed, to a low-degree graph until all admissible vertex pairs of the resulting graph are connected by a path of at most two edges.
- the invention further includes mapping vertices of the resulting graph to nodes of the communication network.
- FIG. 1 is a simplified conceptual diagram of a network for conventional telephony in parallel with a network for internet telephony.
- FIG. 2 is a schematic diagram illustrating signal flow in a network for internet telephony.
- FIG. 3 is a simplified schematic diagram of a network of software switches for internet telephony.
- FIG. 4 is a simplified schematic diagram of a network of three software switches, each containing two call coordinators (CCs). Indicated in the figure are all possible connections between CCs, except that CCs residing in the same switch are not connected. For each possible connection, a probability is indicated, in accordance with the present invention in some embodiments.
- CCs call coordinators
- FIG. 5 is a flowchart of an exemplary procedure for generating a network of CCs according to the invention in some embodiments.
- FIG. 6 is a simplified schematic diagram of a network of four software switches, each containing two CCs, presented as an aide to understanding an alternative network-generating procedure according to the invention in some embodiments.
- FIG. 7 is a flowchart of the network-generation procedure illustrated by FIG. 6 .
- FIG. 8 is a flowchart of a post-processing procedure, according to the invention in some embodiments, for adding links to a network generated by the procedure of FIG. 5 or of FIG. 7 .
- FIG. 9 is a flowchart of a demand-sensitive procedure for network generation according to the invention in some embodiments.
- FIG. 10 is a flowchart of a hybrid method of network generation, according to the invention in some embodiments.
- FIG. 11 is a flowchart of a procedure for assigning physical identities to abstract switches in a load-sensitive manner, according to the invention in some embodiments.
- FIG. 4 which is presented for pedagogical purposes only, is a graph representing a simplified network 110 having three switches S 1 , S 2 , S 3 , each having two CCs.
- the CCs are consecutively numbered N 1 , N 2 , . . . , N 6 . All possible links, numbering twelve in all, are drawn between the admissible pairs. However, a probability p is also indicated in the drawing for each link.
- each of the twelve possible links is added, or not added, in accordance with a loaded coin toss whose probability of a positive outcome is p.
- p probability of a positive outcome
- At least one of the alternative networks will have both: (i) a diameter of two hops; and (ii) a maximum degree that is at most slightly larger than (2n ln n) 1 ⁇ 2 , for example, a maximum degree at most (2.1n ln n) 1 ⁇ 2 .
- the probability of satisfying both of conditions (i) and (ii) approaches unity as n increases.
- the very first network generated will very often satisfy conditions (i) and (ii).
- the probability that any given generated network satisfies conditions (i) and (ii) can also be made to approach unity as n increases. For example, if p is set to [2.05(ln n) / n] 1 ⁇ 2 , the corresponding probability will be at least 1 - ⁇ 1 n 0.05 .
- FIG. 5 is a flowchart of an exemplary procedure for building the random network. It should be noted that this flowchart is meant to be illustrative only, and not limiting, and that numerous alternative procedures will be apparent to those skilled in the art and are envisaged as falling within the scope of the invention.
- each vertex pair is obtained in turn. If the current pair is admissible, as determined at block 120 , then a link is added with probability p, as indicated at block 125 . After the last pair is processed, as determined at block 130 , the procedure exits to, e.g., a post-processing phase as indicated at block 140 and described below.
- the illustrative network 145 of FIG. 6 comprises four switches SI, S 2 , S 3 , S 4 , and eight CCs consecutively numbered N 1 , N 2 , . . . , N 8 .
- the first pair N 1 , N 2 belongs to S 1 , the second pair N 3 , N 4 to S 2 , the third pair N 5 , N 6 to S 3 , and the fourth pair N 7 , N 8 to S 4 .
- the CCs are indexed by the integers 1 - 8 .
- a specified number d′ of distinct random permutations of the CC indices are generated.
- each node identified by an original index is linked directly to the nodes identified by the two corresponding permuted indices, unless the resulting link would connect an inadmissible pair.
- Such an inadmissible pair is N 8 , N 7 , which results by pairing N 8 with its image under the first permutation.
- Table 1 the occurrence of the index 7 in the column corresponding to the first permutation is enclosed in parentheses to indicate that an inadmissible pair is formed.
- FIG. 6 shows that the maximum degree is four, and that such degree occurs for nodes N 4 and N 6 only. Inspection of FIG. 6 also shows that except for nodes N 3 and N 5 , each node lies within at most two hops of each other node that forms with it an admissible pair. However, N 3 is three hops distant from N 8 , and N 5 is three hops distant from N 7 . These distances can be reduced by adding links in a post-processing procedure to be described below.
- a useful value for d′ to be, for example, the greatest integer less than or equal to 0.45 d.
- the network constructed according to the procedure described here will, with certainty, have a maximum degree of no more than 2 d′.
- FIG. 7 is a flowchart of an exemplary procedure for constructing a random graph according to permutations of the nodes. Like FIG. 5, FIG. 7 is meant to be illustrative, and is not meant to exclude from the scope of the invention alternative procedures for achieving essentially the same end result.
- d′ random permutations of the n nodes are generated.
- the permutations are here denominated ⁇ (1) , . . . , ⁇ (d′) .
- a determination is made, for each node in turn, whether the current node and its image under the current permutation form an admissible pair. If they do form an admissible pair, they are connected by drawing an edge between them, as indicated at block 165 .
- the procedure exits to a post-processing phase as indicated at block 175 .
- the post-processing phase will now be described with reference to the flowchart of FIG. 8, which is meant to be illustrative and not to exclude alternate procedures from the scope of the invention.
- the parameter d′ in the procedure of FIG. 7 is designed to provide a moderate shortfall of connectivity between the nodes, it is especially useful in that context to employ a post-processing procedure to supply additional connectivity.
- the post-processing procedure will also be useful in combination with at least some applications of the network-construction procedure of FIG. 5, particularly when the probability p is set to relatively low values.
- each admissible pair of vertices is obtained (block 180 ), and the respective pairs are numbered in random order (block 185 ).
- Each admissible pair is obtained in turn (blocks 190 and 210 ).
- a determination is made (block 195 ) whether more than two hops are required to travel through the network from one member of the pair to the other. The least number of hops required to travel from one member of the pair to the other is here denominated the pair distance. If the pair distance is greater than two, a new edge is added (block 200 ), directly connecting the members of the pair. The procedure ends after the last pair has been processed, as determined at block 205 .
- each time a new edge is added at an iteration of block 200 the distances between other node pairs may be reduced.
- the new edge added between, e.g., nodes A and B will assure a two-hop path between node A and each node directly connected to node B.
- the new edge will assure a two-hop path between node B and each node directly connected to node A.
- adding an edge between the current vertex pair may affect the outcome of test 195 when it is applied to subsequent vertex pairs.
- node-pair randomization of block 185 is useful because it tends to prevent a concentration of added edges in any one particular part of the network. As a consequence, it reduces the likelihood that an excessive number of sockets will be added to any one call coordinator.
- the network-construction procedures described above lead to the best results when the amount of traffic demand is homogeneous, i.e., when it is the same between all pairs of switches.
- demand is not homogeneous, it is useful to construct the network according to a procedure that is sensitive to the individual demands between pairs of switches.
- the total demand for call set-ups between each pair of switches A, B may be divided equally among all pairs of CCs that draw one CC from switch A and one CC from switch B.
- All of the resulting demands between pairs (i,j) of CCs can be expressed as a symmetric demand matrix of respective elements d ij .
- all of the sockets are bidirectional, i.e., that they are fully duplex.
- FIG. 9 is a flowchart of an exemplary procedure for constructing a network having average degree close to A and a variation of degree among the nodes that is sensitive to demand.
- the parameter A can be set arbitrarily. To assure that there will be sufficient aconnectivity, it is preferable not to set ⁇ below about ⁇ square root over (n ln n) ⁇ . To maintain the average degree within practical limits, it is preferable not to set ⁇ above about 3 ⁇ square root over (n ln n) ⁇ .
- FIG. 9 is meant to be illustrative only, and not limiting as to the scope of the invention.
- the ordered pairs of nodes (i,j) are identified (block 215 ), wherein demand is directed from node i to node j. Only admissible pairs are considered. As indicated at blocks 220 and 235 , each admissible pair is considered in turn.
- the calculation of probability p ij takes into account the pertinent element of the demand matrix, the value of the parameter ⁇ , the switch count s, and the number cc of call coordinators per switch.
- each directed link that has been emplaced is replaced by a single undirected link (block 240 ).
- a single undirected link is substituted for both directed links.
- the procedure of FIG. 9 is useful for constructing a network that is responsive to the distribution of demand.
- some distributions of demand may lead to network designs in which the degree of some vertices is excessive.
- some distributions of demand may lead to network designs in which some vertices are separated by more than two hops.
- the hybrid procedure combines aspects of the procedure of FIG. 9, which we here denominate DEM, with aspects of the procedure of FIG. 5 or the procedure of FIG. 7, both of which are specific embodiments of an approach we here denominate UNIF.
- each partition is considered in turn.
- UNIF is used to generate a demand-independent sub-network of average degree ⁇ 1 (block 255 ) and DEM is used to generate a demand-sensitive sub-network of average degree ⁇ 2 (block 260 ).
- the two generated sub-networks are superposed to create a single network that includes all of the edges of both sub-networks (block 265 ). Redundant edges appear only once in the combined network.
- the combined network is evaluated at block 270 for appropriate figures of merit, such as the maximum degree and the total number of sockets.
- one or more combined networks are selected as having the best figures of merit (block 285 ). Exemplarily, such a selection would begin by choosing the networks having diameter at most 2 and least maximum degree. Of the remaining networks, those would be chosen having the least total number of sockets. If more than one combined network has been selected, the selection is narrowed to a single network (block 290 ) by choosing, e.g., that network having the greatest demand-sensitivity, i.e., that having the highest ⁇ 2 .
- the network-construction procedures belonging to the UNIF category produce a network design that is insensitive to individual demand levels between node pairs. Because individual demands are not considered in generating the network, there is no unique association between an abstract switch (i.e., a grouping of same-switch nodes) of the resulting network and a physical switch at a particular location. Instead, the designed network remains at an abstract level, and various mappings are possible of abstract switches to physical switches. In particular, it is possible to make a mapping that assigns abstract switch pairs of relatively high interconnectivity to physical switch pairs of relatively high demand. In this way, some further degree of load-balancing is achieved in the network.
- One measure of interconnectivity between a pair (i,j) of switches is the connectivity coefficient c ij , which is a weighted sum of the number of direct edges between the two switches and the number of two-hop paths between the two switches.
- the direct edge count can be given a larger weight to reflect the fact that direct edges are more desirable because, in general, they will have higher free capacities and smaller delays.
- One relative measure of interconnectivity is the pair load coefficient c ij /d ij .
- the sum, over the network, of all pair load coefficients is a measure of the average number of paths per unit of demand. We denominate this measure the total load measure. Network designs having relatively high values of the total load measure have a greater likelihood that switch pairs with high demands have been given relatively high path diversity.
- each of the s! possible assignments of abstract switches to physical switches can be characterized as a respective permutation of the integers 1 to s.
- each abstract switch i is assigned to the physical switch whose index is the image of i under the pertinent permutation.
- Each permutation can be characterized by a set of s 2 indicator variables x ip having the property that x ip equals 1 if abstract switch i is assigned to physical switch p, and x ip equals zero otherwise. Taken together, the indicator variables form a matrix x.
- FIG. 11 shows a procedure for using the conditional load measure to find an assignment that enjoys a relatively high degree of load balancing.
- FIG. 11 is intended to be illustrative only, and not to limit the scope of the invention.
- the pair load coefficient c ij /d ij is computed for each vertex pair (i,j).
- the conditional load measure £(x) is formulated. The value of £(x) depends upon the particular assignment x of abstract switches to physical switches. It is a standard problem in integer programming to find an assignment x that maximizes an expression of the form assumed by £(x). That standard problem is known as the Quadratic Assignment Problem (QAP).
- QAP Quadratic Assignment Problem
- GRASP Greedy Randomized Adaptive Search Procedure
- the QAP is solved using, e.g., an appropriate heuristic to obtain an assignment x that maximizes, or approximately maximizes, £(x).
- Table 1 shows results obtained using the above-described hybrid procedure that combines aspects of both DEM and UNIF.
- Table 1 shows results obtained using the above-described hybrid procedure that combines aspects of both DEM and UNIF.
- n the number of call coordinators per switch
- d ij uniformly at random in the range [1, 100].
- Table 2 shows results obtained using the hybrid procedure and also incorporating the solution of a QAP problem to assign physical identities to abstract switches in a load-sensitive manner.
- Table 2 shows results obtained using the hybrid procedure and also incorporating the solution of a QAP problem to assign physical identities to abstract switches in a load-sensitive manner.
Abstract
Description
TABLE 1 | |||
| permutation | 1 | |
1 | 5 | 3 | |
2 | 3 | 4 | |
3 | 6 | 2 | |
4 | 8 | 7 | |
5 | 2 | 8 | |
6 | 4 | 1 | |
7 | 1 | 6 | |
8 | (7) | 5 | |
TABLE 1 | |||||
Expt. No. | s | n | Max. Deg. | Ave. Deg. | Min. Deg. |
1 | 10 | 500 | 52 | 46.51 | 40 |
2 | 20 | 1000 | 75 | 68.90 | 60 |
3 | 30 | 1500 | 93 | 86.93 | 76 |
4 | 40 | 2000 | 109 | 101.86 | 89 |
5 | 50 | 2500 | 124 | 115.86 | 101 |
6 | 100 | 5000 | 174 | 168.54 | 157 |
7 | 200 | 10000 | 257 | 247.77 | 241 |
TABLE 2 | ||||
Expt. No. | cc | Max. Deg. | Ave. Deg. | Min. Deg. |
1 | 10 | 56 | 54.35 | 53 |
2 | 20 | 86 | 80.38 | 73 |
3 | 30 | 106 | 100.41 | 92 |
4 | 40 | 126 | 117.92 | 104 |
5 | 50 | 142 | 133.50 | 119 |
Claims (20)
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US09/517,658 US6687363B1 (en) | 2000-03-03 | 2000-03-03 | Method of designing signaling networks for internet telephony |
JP2000168028A JP2001268126A (en) | 2000-03-03 | 2000-06-05 | Method for assigning link between nodes on communication network |
CA002318724A CA2318724A1 (en) | 2000-03-03 | 2000-09-13 | Method of designing signaling networks for internet telephony |
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US09/517,658 US6687363B1 (en) | 2000-03-03 | 2000-03-03 | Method of designing signaling networks for internet telephony |
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US09/517,658 Expired - Fee Related US6687363B1 (en) | 2000-03-03 | 2000-03-03 | Method of designing signaling networks for internet telephony |
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Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
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CN106033342A (en) * | 2015-03-17 | 2016-10-19 | 阿里巴巴集团控股有限公司 | Method and system for generating random graph |
Citations (12)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4704724A (en) * | 1985-12-05 | 1987-11-03 | Bell Communications Research, Inc. | Routing of network traffic |
US4991204A (en) * | 1988-12-05 | 1991-02-05 | Nippon Telegraph And Telephone Corporation | Adaptive routing control method |
US5058105A (en) * | 1990-04-04 | 1991-10-15 | At&T Bell Laboratories | Network alternate routing arrangement |
US5142570A (en) * | 1990-06-15 | 1992-08-25 | Bell Communications Research, Inc. | Routing of network traffic using discrete traffic measurement data |
US5218676A (en) * | 1990-01-08 | 1993-06-08 | The University Of Rochester | Dynamic routing system for a multinode communications network |
US5553206A (en) * | 1993-02-12 | 1996-09-03 | International Business Machines Corporation | Method and system for producing mesh representations of objects |
US5646936A (en) * | 1995-06-22 | 1997-07-08 | Mci Corporation | Knowledge based path set up and spare capacity assignment for distributed network restoration |
US6086619A (en) * | 1995-08-11 | 2000-07-11 | Hausman; Robert E. | Apparatus and method for modeling linear and quadratic programs |
US6154736A (en) * | 1997-07-30 | 2000-11-28 | Microsoft Corporation | Belief networks with decision graphs |
US6331905B1 (en) * | 1999-04-01 | 2001-12-18 | The Trustees Of Columbia University In The City Of New York | Network switch failure restoration |
US6477515B1 (en) * | 1999-08-11 | 2002-11-05 | The United States Of America As Represented By The Secretary Of The Navy | Efficient computation of least cost paths with hard constraints |
US6614762B1 (en) * | 1998-08-10 | 2003-09-02 | International Business Machines Corporation | PNNI topology abstraction |
-
2000
- 2000-03-03 US US09/517,658 patent/US6687363B1/en not_active Expired - Fee Related
- 2000-06-05 JP JP2000168028A patent/JP2001268126A/en not_active Abandoned
- 2000-09-13 CA CA002318724A patent/CA2318724A1/en not_active Abandoned
Patent Citations (12)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4704724A (en) * | 1985-12-05 | 1987-11-03 | Bell Communications Research, Inc. | Routing of network traffic |
US4991204A (en) * | 1988-12-05 | 1991-02-05 | Nippon Telegraph And Telephone Corporation | Adaptive routing control method |
US5218676A (en) * | 1990-01-08 | 1993-06-08 | The University Of Rochester | Dynamic routing system for a multinode communications network |
US5058105A (en) * | 1990-04-04 | 1991-10-15 | At&T Bell Laboratories | Network alternate routing arrangement |
US5142570A (en) * | 1990-06-15 | 1992-08-25 | Bell Communications Research, Inc. | Routing of network traffic using discrete traffic measurement data |
US5553206A (en) * | 1993-02-12 | 1996-09-03 | International Business Machines Corporation | Method and system for producing mesh representations of objects |
US5646936A (en) * | 1995-06-22 | 1997-07-08 | Mci Corporation | Knowledge based path set up and spare capacity assignment for distributed network restoration |
US6086619A (en) * | 1995-08-11 | 2000-07-11 | Hausman; Robert E. | Apparatus and method for modeling linear and quadratic programs |
US6154736A (en) * | 1997-07-30 | 2000-11-28 | Microsoft Corporation | Belief networks with decision graphs |
US6614762B1 (en) * | 1998-08-10 | 2003-09-02 | International Business Machines Corporation | PNNI topology abstraction |
US6331905B1 (en) * | 1999-04-01 | 2001-12-18 | The Trustees Of Columbia University In The City Of New York | Network switch failure restoration |
US6477515B1 (en) * | 1999-08-11 | 2002-11-05 | The United States Of America As Represented By The Secretary Of The Navy | Efficient computation of least cost paths with hard constraints |
Non-Patent Citations (6)
Title |
---|
A. Farago, et al., "Virtual Path Network Topology Optimization Using Random Graphs", Proc. of IEEE INFOCOM '99, pp. 491-496 (1999). |
B. Bollobas, Random Graphs, Academic Press, London, pp. 31-40, 152-155, 228-238 (1985). |
B. D. McKay, et al., "Uniform generation of random regular graphs of moderate degree", Journal of Algorithms, vol. 11, pp. 52-67 (1990). |
N. Alon et al., The Probabilistic Method, Wiley, New York, pp. 95-100, (1992). |
T. A. Feo, et al., "A Greedy Randomized Adaptive Search Procedure For Maximum Independent Set", Operations Research, vol. 42, No. 5, pp. 860-878 (1994). |
T. Luczak, "Sparse random graphs with a given degree sequence", Random Graphs, Wiley, New York, vol. 2, pp. 165-182 (1992). |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN106033342A (en) * | 2015-03-17 | 2016-10-19 | 阿里巴巴集团控股有限公司 | Method and system for generating random graph |
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JP2001268126A (en) | 2001-09-28 |
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